Question

6.4.4

Annual rainfalls for Sydney, Australia are given in table #6.4.6. ("Annual maximums of," 2013). Can you assume rainfall is normally distributed?

Table #6.4.6: Annual Rainfall in Sydney, Australia

146.8	383	90.9	178.1	267.5	95.5	156.5	180
90.9	139.7	200.2	171.7	187.2	184.9	70.1	58
84.1	55.6	133.1	271.8	135.9	71.9	99.4	110.6
47.5	97.8	122.7	58.4	154.4	173.7	118.8	88
84.6	171.5	254.3	185.9	137.2	138.9	96.2	85
45.2	74.7	264.9	113.8	133.4	68.1	156.4

6.5.2

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.

1. If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? Why?
2. For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean.
3. For a sample of size 10, find the probability that the sample mean is more than 241.
4. If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why?
5. For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.
6. For a sample of size 35, find the probability that the sample mean is more than 241.
7. Compare your answers in part c and f. Why is one smaller than the other?

Answer 1